Second-largest cities
A while back I was in the local coffee shop and mentioned that my wife
had been born in Rochester, New York. "Ah," said the server. "The
third-largest city in New York." Really? I would not have guessed
that. (She was right, by the way.) As a native of the first-largest
city in New York, the one they named the state after, I have spent
very little time thinking about the lesser cities of New York. I
have, of course, heard that there are some. But I have hardly any
idea what they are called, or where they are.

It appears that the
second-largest city in New York state is some place called (get this)
"Buffalo". Okay, whatever. But that got me wondering if New York was
the state with the greatest disparity between its largest and
second-largest city.
Since I had the census data lying around from a related project (and a
good thing too, since the Census Bureau website moved the file) I
decided to find out.

The answer is no. New York state has only one major city, since its
next-largest settlement is Buffalo, with 1.1 million people.
(Estimated, as of 2006.) But the second-largest city in Illinois is
Peoria, which is actually
the punchline of jokes. (Not merely because of its small size;
compare Dubuque, Iowa, a joke, with Davenport, Iowa, not a joke.) The
population of Peoria is around 370,000, less than one twenty-fifth
that of Chicago.

But if you want to count weird exceptions, Rhode Island has everyone
else beat. You cannot compare the sizes of the largest and
second-largest cities in Rhode Island at all. Rhode Island is so
small that it has only one city, Seriously. No, stop laughing! Rhode
Island is no laughing matter.

The Articles of Confederation required unanimous consent to amend, and
Rhode Island kept screwing everyone else up, by withholding consent,
so the rest of the states had to junk the Articles in favor of the
current United States Constitution. Rhode Island refused to ratify
the new Constitution, insisting to the very end that the other states
had no right to secede from the Confederation, until well after all of
the other twelve had done it, and they finally realized that the
future of their teeny one-state Confederation as an enclave of the
United States of America was rather iffy. Even then, their vote to
join the United States went 34–32.

But I digress.

Actually, for many years I have said that you can impress a Rhode
Islander by asking where they live, and then—regardless of what
they say—remarking "Oh, that's near Providence, isn't it?" They
are always pleased. "Yes, that's right!" The census data proves that
this is guaranteed to work. (Unless they live in Providence, of
course.)

Here's a joke for mathematicians. Q: What is Rhode Island? A: The
topological closure of Providence.

Okay, I am finally done ragging on Rhode Island.

Here is the complete data, ordered by size disparity. I wasn't sure
whether to put Rhode Island at the top or the bottom, so I listed it
twice, just like in the Senate.

State

Largest city and its Population

Second-largest city and its population

Quotient

Rhode Island

Providence-New Bedford-Fall
River

1,612,989

—

Illinois

Chicago-Naperville-Joliet

9,505,748

Peoria

370,194

25

.68

New York

New York-Northern New Jersey-Long Island

18,818,536

Buffalo-Niagara Falls

1,137,520

16

.54

Minnesota

Minneapolis-St. Paul-Bloomington

3,175,041

Duluth

274,244

11

.58

Maryland

Baltimore-Towson

2,658,405

Hagerstown-Martinsburg

257,619

10

.32

Georgia

Atlanta-Sandy Springs-Marietta

5,138,223

Augusta-Richmond County

523,249

9

.82

Washington

Seattle-Tacoma-Bellevue

3,263,497

Spokane

446,706

7

.31

Michigan

Detroit-Warren-Livonia

4,468,966

Grand Rapids-Wyoming

774,084

5

.77

Massachusetts

Boston-Cambridge-Quincy

4,455,217

Worcester

784,992

5

.68

Oregon

Portland-Vancouver-Beaverton

2,137,565

Salem

384,600

5

.56

Hawaii

Honolulu

909,863

Hilo

171,191

5

.31

Nevada

Las Vegas-Paradise

1,777,539

Reno-Sparks

400,560

4

.44

Idaho

Boise City-Nampa

567,640

Coeur d'Alene

131,507

4

.32

Arizona

Phoenix-Mesa-Scottsdale

4,039,182

Tucson

946,362

4

.27

New Mexico

Albuquerque

816,811

Las Cruces

193,888

4

.21

Alaska

Anchorage

359,180

Fairbanks

86,754

4

.14

Indiana

Indianapolis-Carmel

1,666,032

Fort Wayne

408,071

4

.08

Colorado

Denver-Aurora

2,408,750

Colorado Springs

599,127

4

.02

Maine

Portland-South Portland-Biddeford

513,667

Bangor

147,180

3

.49

Vermont

Burlington-South Burlington

206,007

Rutland

63,641

3

.24

California

Los Angeles-Long Beach-Santa Ana

12,950,129

San Francisco-Oakland-Fremont

4,180,027

3

.10

Nebraska

Omaha-Council Bluffs

822,549

Lincoln

283,970

2

.90

Kentucky

Louisville-Jefferson County

1,222,216

Lexington-Fayette

436,684

2

.80

Wisconsin

Milwaukee-Waukesha-West Allis

1,509,981

Madison

543,022

2

.78

Alabama

Birmingham-Hoover

1,100,019

Mobile

404,157

2

.72

Kansas

Wichita

592,126

Topeka

228,894

2

.59

Pennsylvania

Philadelphia-Camden-Wilmington

5,826,742

Pittsburgh

2,370,776

2

.46

New Hampshire

Manchester-Nashua

402,789

Lebanon

172,429

2

.34

Mississippi

Jackson

529,456

Gulfport-Biloxi

227,904

2

.32

Utah

Salt Lake City

1,067,722

Ogden-Clearfield

497,640

2

.15

Florida

Miami-Fort Lauderdale-Miami Beach

5,463,857

Tampa-St. Petersburg-Clearwater

2,697,731

2

.03

North Dakota

Fargo

187,001

Bismarck

101,138

1

.85

South Dakota

Sioux Falls

212,911

Rapid City

118,763

1

.79

North Carolina

Charlotte-Gastonia-Concord

1,583,016

Raleigh-Cary

994,551

1

.59

Arkansas

Little Rock-North Little Rock

652,834

Fayetteville-Springdale-Rogers

420,876

1

.55

Montana

Billings

148,116

Missoula

101,417

1

.46

Missouri

St. Louis

2,796,368

Kansas City

1,967,405

1

.42

Iowa

Des Moines-West Des Moines

534,230

Davenport-Moline-Rock Island

377,291

1

.42

Virginia

Virginia Beach-Norfolk-Newport News

1,649,457

Richmond

1,194,008

1

.38

New Jersey

Trenton-Ewing

367,605

Atlantic City

271,620

1

.35

Louisiana

New Orleans-Metairie-Kenner

1,024,678

Baton Rouge

766,514

1

.34

Connecticut

Hartford-West Hartford-East Hartford

1,188,841

Bridgeport-Stamford-Norwalk

900,440

1

.32

Oklahoma

Oklahoma City

1,172,339

Tulsa

897,752

1

.31

Delaware

Seaford

180,288

Dover

147,601

1

.22

Wyoming

Cheyenne

85,384

Casper

70,401

1

.21

South Carolina

Columbia

703,771

Charleston-North Charleston

603,178

1

.17

Tennessee

Nashville-Davidson--Murfreesboro

1,455,097

Memphis

1,274,704

1

.14

Texas

Dallas-Fort Worth-Arlington

6,003,967

Houston-Sugar Land-Baytown

5,539,949

1

.08

West Virginia

Charleston

305,526

Huntington-Ashland

285,475

1

.07

Ohio

Cleveland-Elyria-Mentor

2,114,155

Cincinnati-Middletown

2,104,218

1

.00

Rhode Island

Providence-New Bedford-Fall
River

1,612,989

—

Some of this data is rather odd because of the way the census bureau
aggregates cities. For example, the largest city in New Jersey is Newark.
But Newark is counted as part of the New York City metropolitan area,
so doesn't count separately. If it did, New Jersey's quotient would be
5.86 instead of 1.35. I should probably rerun the data without the
aggregation. But you get oddities that way also.

I also made a scatter plot. The x-axis is the population of
the largest city, and the y-axis is the population of the
second-largest city. Both axes are log-scale:

Nothing weird jumps out here. I probably should have plotted
population against quotient. The data and
programs are online if you would like to mess around with them.